Efficient Implementation of Fourier Modal Method for 2-D Periodic Structures

The conventional Fourier modal method (FMM) has the problems of large memory requirements and low computational efficiency in analyzing 2-D periodic structures. In this letter, a highly symmetric system matrix formulation of the FMM is presented. The conventional FMM is enhanced by using an improved system matrix incorporated with the Cayley–Hamilton theorem. This makes the FMM more efficient in analyzing 2-D periodic structures. Numerical results agree well with those of published literature and the conventional methods. Simulation results show that, compared with the conventional FMM, the proposed method can significantly reduce the memory requirements and condition number while keeping high accuracy.